Multistate coherent systems of order k

Abouammoh, A. M.; Al-Kadi, M.A.

doi:10.1016/0026-2714(94)00157-j

Cited by 4 publications

(2 citation statements)

References 14 publications

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“…To assume that the system S and its elements e e e n 1 2 , ,..., can only be in either state Usually, the elements of the Z i are real numbers. Otherwise, a total order in the set Z Z Z 1 2 ∪ ∪ ∪ L n must be given (see, for instance, [1,11,19]). In these papers it is generally assumed that the state spaces Z s and Z i are identical or r s = 2 and r i > 2 .…”

Section: Multivalued Systemsmentioning

confidence: 99%

Disjoint sum forms in reliability theory

Anrig¹,

Beichelt²

2014

ORiON

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The structure function ϕ of a binary monotone system is assumed to be known and given in a disjunctive normal form, i.e. as the logical union of products of the indicator variables of the states of its subsystems. Based on this representation of ϕ, an improved Abraham algorithm is proposed for generating the disjoint sum form of ϕ. This form is the base for subsequent numerical reliability calculations. The approach is generalized to multivalued systems. Examples are discussed.

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Section: Multivalued Systemsmentioning

confidence: 99%

Disjoint sum forms in reliability theory

Anrig¹,

Beichelt²

2014

ORiON

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“…lt is interesting that their research was initiated by solving problems arising from the 'theory of artificial intelligence. Recent contributions to multivalued coherent systems gave BAXTER [11,12], MAZARS [13], MENG [14] as well as ABOUAMMOH and AL-KADI [15].…”

Section: Binary Coherent Systemsmentioning

confidence: 99%

Some current problems in reliability theory

Beichelt¹

2003

ORiON

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Reliability work occupies an increasingly important place in engineering practice. Although the details differ depending on whether mechanical, electrical, chemical, or other systems are under analysis, the reliability concepts and the mathematical foundations cut across the specific fields of application. Over the past 50 years thousands of papers and dozens of books on mathematical models of reliability have been published. A comprehensive survey alone on the current developments in the mathematical theory of reliability would fill a voluminous book. Based on importance both for theory and application and taking into account the interests of the author, current investigations in four important branches of reliability theory are considered: coherent systems, stochastic networks, software reliability, and maintenance theory. *) Invited plenary lecture at the Annual Conference of the German Statistical Society and the Stochastic Society within the German Mathematical Association, Wittenberg (Germany), May 1997. http://orion.journals.ac.za/

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On system reliability approaches: a brief survey

Ram

2013

Int J Syst Assur Eng Manag

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Multistate coherent systems of order k

Cited by 4 publications

References 14 publications

Disjoint sum forms in reliability theory

Disjoint sum forms in reliability theory

Some current problems in reliability theory

On system reliability approaches: a brief survey

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